Applying animated compositor to pre-rendered animation frames
There doesn't need to be a big change, the compositor can read a sequence of images just as easily as a single image.

I would recommend saving your render files as openexr multilayer. The files are larger but they can include all render layers and output sockets that you normally use in the compositor. If you specify a full filename remember to add some #'s to get a frame number included.

After saving your animation frames, create a new scene and in the compositor start with an Input->Image node and open all of your images. This leaves you with one scene to do the heavy rendering and one for only compositing and it's all in the one blend file. As the same nodes will apply to the entire sequence you may want to create several scenes for compositing to get different effects in different shots of your animation.